We present new Hubble Space Telescope/Wide Field Camera 3 imaging of 25 extremely luminous (−23.2 ≤ M UV −21.2) Lyman-break galaxies (LBGs) at z 7. The sample was initially selected from 1.65 deg 2 of ground-based imaging in the UltraV-ISTA/COSMOS and UDS/SXDS fields, and includes the extreme Lyman-α emitters, 'Himiko' and 'CR7'. A deconfusion analysis of the deep Spitzer photometry available suggests that these galaxies exhibit strong rest-frame optical nebular emission lines (EW 0 (Hβ + [OIII]) > 600Å). We find that irregular, multiple-component morphologies suggestive of clumpy or merging systems are common ( f multi > 0.4) in bright z 7 galaxies, and ubiquitous at the very bright end (M UV < −22.5). The galaxies have half-light radii in the range r 1/2 ∼ 0.5-3 kpc. The size measurements provide the first determination of the size-luminosity relation at z 7 that extends to M UV ∼ −23. We find the relation to be steep with r 1/2 ∝ L 1/2 . Excluding clumpy, multi-component galaxies however, we find a shallower relation that implies an increased star-formation rate surface density in bright LBGs. Using the new, independent, HST /WFC3 data we confirm that the rest-frame UV luminosity function at z 7 favours a power-law decline at the bright-end, compared to an exponential Schechter function drop-off. Finally, these results have important implications for the Euclid mission, which we predict will detect > 1000 similarly bright galaxies at z 7. Our new HST imaging suggests that the vast majority of these galaxies will be spatially resolved by Euclid, mitigating concerns over dwarf star contamination.